Determination of the ν4 band strength of 12CH4 from diode laser line strength measurements

JOURNAL

OF MOLECULAR

SPECTROSCOPY

94, 369-379

(1982)

Determination of the v4 Band Strength of 12CH4from Diode Laser Line Strength Measurements D. E. JENNINGS' NASA

Goddard

Space Flight Center, Greenbelt.

Maryland

20771

AND A. G. ROBIETTE Department

of Chemistry,

University

of Reading,

Reading

RG6 2AD. United Kingdom

The strengths of over 50 lines in the Y.,region of ‘%H, were measured using a diode laser spectrometer. Forty-nine lines were assigned to transitions of the Ye band. Analysis of the strengths of these 49 lines leads to a value of the integrated band strength Sy = 127 f 4 cm-* atm-’ at 295.7 K; this value is compared to other recent band strength determinations. The Herman-Wallis factor, expressing the dependence of the transition moment on rotational quantum number, is also discussed. INTRODUCTION

Published values for the v4 integrated band strength of methane cover a wide range. In a review of the literature up to 1978, Chedin et al. (I) gave values ranging from 103 cm-’ atm-’ at 300 K (2) to 168 cm-* atm-’ at 300 K (3). They showed, however, that almost all other determinations fell within the range 132- 147 cm-* atm-’ at 300 K, and adopted 140 cm-’ atm-’ at 300 K as the most probable value of the v4 band strength. More recent experimental work has not helped to clarify the situation. On the one hand, band strengths derived from tunable diode laser line strength measurements provided values of 104 +- 6 cm-* atm-’ at 300 K (4) and 116 f 3 cm-* atm-’ at 300 K (5) apparently supporting the low value of 103 cm-’ atm-’ at 300 K earlier favored by Fox and Person (2). At the other extreme, a line-by-line intensity analysis (6) of the 1100-l 800 cm-’ methane atlas compiled by Blatherwick et al. (7) gave a u4band strength of 166 + 17 cm-* atm-’ at 300 K, apparently confirming the high value of 168 cm-* atm-’ at 300 K measured by Burch and Williams (3). In between, Bode and Smit obtained 129 + 2 cm-* atm-’ at 300 K (8), while Varanasi and Ko (9) presented new experimental evidence confirming the value of 132 + 7 cm-* atm-’ at 300 K measured by Ko and Varanasi (IO). The purpose of the present paper is to present new diode laser line intensity measurements in the v4 band of ‘*CH,. These measurements refine and extend the ’ The NASA-Goddard Atmospheres Program.

Space Flight

Center

part of this work was supported

369

by the NASA

Planetary

0022-2852/82/080369-l

1$02.00/O

Copyright

Press, Inc.

Q 1982 by Academic

All rights of reproduction

in any form reserved.

370

JENNINGS

%

AND

ROBIETTE

y : P+(13) F, (3)

1218.625

cm-’

FIG. 1. A typical recording showing the signal-to-noise methane line. The experimental conditions are as indicated

ratio and the near-Gaussian on the figure.

shape of the

data previously reported by Jennings (I 1): the number of lines studied and the range of J values are both much larger than in the two other diode laser investigations cited above (4,5). The intensity data have been analysed using a theoretical model of the Coriolis-coupled v2 and v4 bands, which reproduces the known line positions almost to within experimental accuracy (Z2). EXPERIMENTAL

DETAILS

The diode laser spectrometer and the technique for determining line strengths have been described previously (I 1). The collimated laser beam was shuttered at -30 Hz using a rotating butterfly chopper, and the laser injection current was sawtooth modulated synchronously with the chopper. Successive sweeps through the spectrum were integrated with a signal averager. An example of the resulting spectra is shown in Fig. 1. The shutter action of the chopper permits simultaneous recording of the zero and full transmission levels along with the spectrum of the absorption line. This method of sweep integration produces high signal-to-noise ratios in relatively short scan times. For the stronger low-J transitions in v4 the gas sample was placed in a 3.0-, lO.O-, or 30.0-cm straight-path absorption cell. For the weaker high-J transitions a 31-cm White cell was used at various path lengths: 129.5, 253.8, 502.4, and 1248.2 cm. The methane sample was of natural isotopic composition, i.e., 98.9% rZCH4. Sample pressures, measured with a Baratron capacitance manometer, were usually between 0.1 and 0.7 Torr and always less than 1.1 Torr. Cell temperature was ambient and was measured with an accuracy of approximately kO.5 K. Each line was recorded several times and the results were averaged. The 100% absorption level was checked at high sample pressures and long path lengths. The line strengths were found from line center absorptions as described in Ref. (II ). Each measurement was corrected for r2CH4 abundance and for effects of sample pressure and diode laser lineshape on line center absorption. The CH,-CH, broadening parameter was taken as 0.08 cm-’ atm-’ (13), and the resulting corrections due to pressure were in the range 0.6 to 5.4%.

v4 BAND STRENGTH

OF ‘*CHd

371

In correcting the measured strengths for laser effects the laser lineshape was considered to be approximately Lorentzian (14). The extended wings of a Lorentzian instrument profile can cause a significant reduction in absorption at line center while producing little line broadening as measured at half-maximum absorption. The source of excess linewidth in diode lasers is not well understood, although it cannot be due entirely to refrigerator vibrations since it is also observed when the diode is operated on a liquid helium Dewar (15). Heterodyne studies of diodes show that laser linewidths are generally about ~-MHZ FWHM or greater (see, for example (14-Z@), and comparison of the recorded widths of several of our transitions with their calculated Doppler widths limits the laser linewidths in this experiment to ~7 MHz. We therefore corrected our measurements for a Lorentzian instrument profile of width 5 + ~-MHZ FWHM. The strength correction, 5.4 + 2.0%, was based on the analysis by Strow (17) and was appIied to all measurements. The 2.0% error limits were combined with the measurement error for each line. The measured line strengths are listed in Table I. Among those tabulated are 11 transitions which were measured previously (I I ), and of these 7 were remeasured for the present analysis. The results of the old and new measurements were combined, taking into account the different sample temperatures. The corrections discussed above were applied to both old and new measurements. The line positions quoted were taken from Fourier transform spectra (Z8) which had been calibrated against diode laser measurements in v4, the latter in turn calibrated using N20 lines as standards (19). We have assigned the P ‘(20) A I’), F’,‘), and E(lf blend to the line at 1 I 87.720 cm-‘. Two lines near 1 I 87.3 cmTr and one near 117 1.O cm-’ have not been assigned. THEORY

In essence the treatment of the line strength data follows closely the development of Dang-Nhu et al. (201, which in turn is in many respects based on that of Fox and Person (2). The theoretical line strength Sit from an initial state i to a final state f is expressed as 4, = SzR&F,

(1)

where S$ is the integrated band strength, R;ta factor depending on the initial and final rotational states, vi the “eigenvector factor” which depends on the extent to which each transition is enhanced or depleted by vibration-rotation mixing effects, and F is the “Herman-Wallis factor” containing the rn dependence of the transition moment. Detailed equations for each of the factors are given by Dang-Nhu et al., and we give only brief details here. The analysis was carried out for a temperature of 295.7 K, the temperature at which the majority of the intensity measurements were made. At this temperature, the integrated band strength S$ is related numerically to the vibrational transition moment (pq) by S!/cm-2

atm-’ = 40 375.3 ((~~)/~)*.

(2)

372

JENNINGS

AND ROBIETTE TABLE I

Measured Line Strengths in the v, Band of “CH, Assignment

-I cm

-2-l cm

1316.826 1311.428 1267.819 1263,.331 1243.351 1242.661 1236.029 1236.008 1235.954 1235.925 1230.286 1230.080 1229.998 1229.962 1223,357 1223. I53 1220.857 1218.625 1216.627 1216,326 1216:196 1210.782 12lOi670 1210.075 1210~004 1207,830 1202.722 1202.419

1198.998 1194.954 1191.474 1191.429 1188.997 1188.952 1187.720 1187i338 1187.300 1 l85;690 1184.468 1179.820 1177.870 1177.786 1177.741 1176.212 1176.198 1174.106 1173.796 1173.644 li72.594 1170.987 1170.900 1170.430 a b

Ref,

R-(l)

R-(O) P+(6) P+(7) P*(iOf P+(iO) P*fll)

P+(12) P+(iZf P+(lz) P+(il) P’(i2) P+(l3) P+(i3) P+fl3) P+(131 P+flZ) P+(i3) P*(l4) P+(i4) P+113) P*(l4) P+(13) P+f14) P+(lS) P+(l4) P+(l5) P+(i4) P+(lS) P+(ld) P+(lS) P+(i6) P+(17) P+(16) P+(20)

FI(1) Al(l) Al(i) A2(l) F2f21 Flfl) E(l) Al(i) F&(I) E(l) FZ(3) F2(i) FICI) FZ(i) E(l) Ff (2) F2f3) Flf3) F2(2) Fl(1) A2(1) FlfZ) F1f4f E(2) A2(l) F2(3) FZ(3) FI (3) Fl(3) A2(l) F2(4) FZ(3f Fl(3) Alf2) Al ,Fl ,E

P’fl I) P+(l7f P+(i7) P”(li) P”(ll) P’(Ii) P*(20) P+(20) P+(l9) P+(l9) P+(l8) P’(12)

Ft (2) A2(1)

P+(l?) P+07)

E(3) Fl(5)

Fi(4)

AZ(i) F2(2f E(l) F2(l) FI (2) FI (2) F2(3) Fi(3) A2(1)

b

Strength

Temperature

am

K

I .084(23) 1.066(23) 1.44flO) I. 105(353 0.259(&j 0.252(9) 0.1068(32) 0.166(S) 0.1012(30) 0.066909) 0.148(5) 0.0866(39) 0.0538(17) 0.0534(16) 0.036ifi4) 0.0552(16) 0.0922f27f 0.0528fl5) 0.0296(10) 0.0296 (9) 0.0855(24) 0,0277(14f 0.0497(25) 0.0178(7) 0.0225(9) 0.0265(10) 0.0132(6) O.O26S(li) 0.0129(5) 0.0114(3) 0.013Sf4) 0.00634(18) 0.00315(14) 0.01058(29) 0.000798(22~ 0.000236(21) 0.000194(18~ 0.00209(6) 0.00473fi6) 0.00284(Y) 0.00437(13) 0.00231(7) 0.00145(8) 0.000202 (I 6) 0.000211(13) O.OOOSZS(23) 0.000538(21) 0.00123f71 0.0016ifi3) 0.000471(35) 0.00185(11) 0.00282(8)

295.2 295.2 298.9 299.2 299.2 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 295.7 296.2 295.7 295.7 296.2 295.7 295.7 295.7 295.7 295.7 294.7 294.7 294.7 295.7 295.7 295.7 295.7 295.7 295.7 294.7 294.7 294.7 294.7 294.7 295.7 294.7 294.7 295.7

(I@

Corsected for pressure and laser lineshape (see text>. Uncertainties in parentheses

effects refer

and for to

the

last

isotopic digit

abundance quoted.

The quantity Rif is the factor .Rif= (Yif/Ve)ti(2Jt + 1)

eXp(-hC&/kT)[

1-

eXp(-hCVif/kT}]/32~

*

(3)

with V4being the band center, ei the spin statistical weight of the initial level, and

373

u4BAND STRENGTH OF ‘*CH,

Z, the rotational partition function; other symbols have their usual significance. The value of Z, was taken to be 585.693 at 295.7 K (21). The eigenvector factor vi’fwas taken from the recent calculation by Robiette (12). Numerical values of vfr are given below. The calculation takes account of vibration-rotation mixing between the IL, = 1 and n2 = 1 states through the rz., Coriolis interaction and some higher-order mixing terms. Interactions of the u4 = 1 state with vibrational states other than u2 = 1 must be absorbed empirically by the Herman-Wallis F factor, which Dang-Nhu et al. (20) wrote as a power series E;=1+a,mi-cY,m2+

****

(4)

The most important contribution to the m-dependent terms of F is the fS4 Coriolis interaction (22). If this were the only mechanism contributing to the F factor, then F could be written in the simpler form +C,m)‘,

F=(l

with C, given theoretically

(5)

by @

4~S34(w4)‘f2

(114)

tw: - &I

* I

(6)

In practice there are other mechanisms which contribute to the nt2 and higherorder terms of Eq. (4), so it is not clear whether it is better to treat cy2 as an adjustable parameter or to constrain F to follow Eq. (5) when fitting experimental data (20, 22). RESULTS

The measured line strengths given in Table I were converted to a common basis by making small temperature corrections to all strengths not measured at 295.7 K. These corrections were calculated from the temperature-dependent factors in Eqs. (l-6) of Dang-Nhu et al. (20), although virtually the same results are obtained from the temperature dependence of Eq. (6) of Fox et al. (4). The corrected line strengths were used as input to a least-squares calculation, each strength being weighted as the inverse square of its experimental uncertainty given in Table I. All 49 lines assigned to “CH, transitions were used. In the case of the P ‘(20) blend at 1187.720 cm-‘, the individual components are calculated to be virtually coincident (12) and the three contributing calculated line strengths were added to form the calculated composite strength for the blend. Initially the Herman-Wallis factor was taken as F = (1 + C4m)2, so that the only two adjustable parameters in the intensity model were $2 and C,. The parameter values derived from the fit were Si = (127.4 +- 2.0) cmP2 atm-’ at 295.7 K,

(7)

C, = -0.0067

(8)

f 0.0006.

This value of C4 differs appreciably from the theoretical value: calculating (p4) from Eqs. (2) and (7) and taking the other quantities in Eq. (6) from Dang-Nhu

374

JENNINGS

AND

ROBIETTE

et al. (20), we obtain’ C4(calc) = -0.00375 . Because of this discrepancy an alternative two-parameter vestigated. Equation (4) may be rewritten

(9) intensity model was in-

F = (1 + C,m)’ + Cbrn’.

(10)

This version of the Herman-Wallis factor was applied with C, constrained to the calculated value of Eq. (9), and S9 and the m2 coefficient Cb treated as adjustable parameters, with results as follows3: ,!?i = (127.2 f 1.5) cms2 atm-’ at 295.7 K,

(11)

c: = (4.5 f 0.7) x 10-4.

(12)

This parameterization in fact gives a significantly better fit to the intensity data, and because it is consistent with the theoretical magnitude of the Herman-Wallis factor as far as the linear m coefficient is concerned we choose this model for the subsequent discussion. Table II compares the observed line strengths with those calculated from the model of Eqs. (10-12). Because of the wide range of strengths, the experimental uncertainties and the residuals are both quoted as percentages. The table also gives the ufr factors relevant to Eq. (1). Several points deserve comment. (i) The J values studied range from 0 to 20 and consequently the line strengths also cover a wide range. The estimated uncertainties are generally from 2 to 5% rather more for a few weak lines or in regions where the diode performance was less reproducible. In the great majority of cases the line strengths are fitted to better than 5%: the unweighted rms percentage deviation for the 49 data points is 3.9%. Omitting the few really poor lines (e.g., P+(12) F,(l) at 1230.09 cm-‘) caused only insignificant changes in the intensity parameters, and so we prefer to give the results for all lines studied. (ii) The I$ factors of the formally allowed branches P+(J) and R-(J) range from 1.00 in the case of R -(O), which is not perturbed by the ~2/~4 Coriolis mixing, to 0.79 in the case of P’( 18) F,( 13). This means that the latter line has lost over 20% of the intensity calculated in a first-order model (4). The lost intensity is transferred mainly to y2 transitions? but also to some degree to the formally forbidden P” and P- transitions in v4. It is clear that the vi: factors must be included in any accurate treatment of the line strengths, unless the data are restricted to very low J values. (iii) Our data include five “forbidden” transitions from the P” branch, with intensities around 1 to 2% of the “allowed” transitions of corresponding J. These transitions are fitted with much the same percentage error as for the bulk of the ’ The previous estimate of Cd(calc) was -0.0034 (20, the transition moment (pd) derived indirectly (20) and strength. 3 The simultaneous refinement of Si, C,, and C; was were so highly correlated that the standard deviations of as the constants themselves.

22). This calculation, however, used a value of not from a direct measurement of the v., band also attempted, but in this case the parameters C., and C!, were of the same order of magnitude

v4 BAND STRENGTH

375

OF “CHs

TABLE II Comparison of Observed and Calculated Line Strengths in the vg Band of “CH.,. The Observed Strengths are Corrected to 295.7 K Where Necessary, and the Calculated Strengths Are Based on Eqs. (9-12) Assignment

S(obs) cm

-2

am

S(calc) -I

cm

R-(l) R-(O)

Fi(1) Al(l)

I .079 1,061 1.463 1.120 0.258 0.252 0.1068 0.1660 0.1012 0.0669 0.1480 0.0866 0.0538 0.0534 0.0361 0.0552 0.0922 0.0528 0.0294 0.0296 0.0855 0.0277 0.0497 0.01780 0.0225 0.0264 0.01320 0.0265 0.01280 0.01140 0.01350 0.00634 0.00315 0.01058 0.000820 0.00209 0.00473 0.00286 0.00437 0.00231 0.001450 0.000208 0.000217 0.000541 0.000551 0.001260 0.001610 0.001880 0.00282

P:(6) P-(7) P+(Io) P+(ioj P+(ll) P+(l2) P+(12) P+(12) P+(l I) P+(12) P+(l3) P’(13)

Al 0) A2(1) P2(2) FI(I~ E(1) Al(I) Fl(I) E(I) FZ(3) F2(1) Fl(t) FZ(l)

Ptfl3) P-(13) P+
E(l) Fl(2) F213) F1 i3j F2(2f F](l) A2(1) Fl(2) FI (4) E(2) AZ(l) FZ(3) F2(3) Fl(3) Fl(3) AZ(l) FZ(4) PZ(3) Fl(3) Al (2) Al .Fl ,E Fli2)A2(1) F](4) A2ilj F2(2) E(l) F?_(l) FIG!) Fl(2) F2(3) Fl(3) A2(1) E(3) Fi (5)

Note:

A is the residual Cobs-c&c) experimental uncertainty from * is defined in the text. “if

-2

atm

A(X)

o(X)

5.4 -1.5 6.4 -1.3 1.9 0.2 0.3 -2.2 -0.5 -1.4 -5.5 -10.8 -7.5 -8.3 0.0 2.1 0.i 1.3 1.7 2.7 -0.1 0.6 -3.5 -2.7 -8.3 -2.4 -4.2 -2.0 -4.9 4.8 0.3 -0.4 5.5 1.2 0.6 3.0 -1.4 2.4 4.9 3.5 1.4 -4.8 -0.4 4.3 6.5 5. I 0.2 -0.1 -0.3

2.1 2.2 6.8 3. I 3.1 3.6 3.0

2 “if

-I

I.021 1.077 1.369 I.135 0.253 0.252 0.1064 0.1697 0.1017 0.0678 0. IS62 0.0959 O.OS78 0.0578 0.0361 0.0540 0.0921 0.0521 0.0289 0.0288 0.0856 0.0275 0.0514 0.01827 0.0244 0.0270 0.01375 0.0270 0.01343 0.01085 0.01346 0.00636 0.00298 0.01046 0.000815 0.00203 0.00480 0.00279 0.00416 0.00223 0.001430 0.000218 0.000218 0.000518 0.0005 I5 0.001196 0.001606 0.001881 0.00283

expressed Table I

3.0 3.0 2.8 3.4 4.5 3.2 3.0 3.9 2.9 2.9 2.8 3.4 3.0 2.8 5.1 5.0 3.9 4.0 3.8 4.5 4.2 3.9 2.6 3.0 2.8 4.4 2.7 2.7 2.9 3.4 3. I 3.0 3.0 5.5 7.7 6.0 4.3 3.8 5.6 8.1 5.9 2.8

as a percentage of SCobs); expressed 88 a percentage of

0.9993 I . 0000 0.9787 0.9715 0.9504 0.9447 0.9390 0.9877 0.9871 0.9868 0.9237 0.9362 0.9856 0.9852 0.9290 0.9273 0.9069 0.8983 0.9216 0.9191 0.8872 0.8836 0.8936 0.8801 0.9153 0.8699 0.8676 0.8747 0.8504 0.8523 0.8589 0.8361 0.8506 0.8264 0.9694 0.0124 0.8263 0.8054 0.0154 0.0138 0.0146 0.8780 0.8778 0.8270 0.8233 0.7947 0.0099 0.8222 0.8245

0 is the S(obs);

data. The good quantitative agreement between observed and calculated intensities provides confirmation of the quality of the vibration-rotation model used. Finally, we note that in the fit quoted, the C> coefficient given in Eq. ( 12) is perhaps a little larger than anticipated from order-of-magnitude considerations. In

376

JENNINGS

AND ROBIETTE

TABLE III Intensity Parameters

Derived from Various Least-Squares

J” (Inax)

20

-2 -1 S,Oic* atm at 295.7 K

127.2 (1.5)

Fits to the Observed Line Strengths

C4

-0.00375

C4'

0.00045(7)

20

127.4 (2.0)

-0.006?(6)

0

18

128.6 (2.0)

-0.006117)

0

16

129.4 (2.0)

-0.0055(7)

0

14

130.2 (1.9)

-0.0050(7)

0

12

130.4 (2.0)

-0.0049(E)

0

12+

130.2 (1.9)

-0.0043(8)

0

Note:

Figures in parentheses are one standard deviation in the least significant digit. where no error is given, the parameter was constrained. C,,and C,,'me defined in eq. (IO).

t

In this fit the "forbidden" lines of the PO branch were omitted.

physical terms, the P-branch lines at the highest J values are systematically higher in intensity than the theoretical Herman-Wallis factor ( 1-0.00375m)2 would predict. This can also be seen from results given in Table III, which shows the parameters derived from fits using the Herman-Wallis factor (1 + C,ruz)” but restricting the upper limit on J. As the high J lines are excluded, the refined value of C, progressively approaches the theoretical value. At the same time there is a systematic change in the refined value of S:, so that the unexplained effects at high J may introduce some systematic uncertainty into the derived band strength. We judge therefore that the best value of the band strength is that obtained from the full range of data (largely independent of the form of Herman-Wallis factor, cf. Eqs. (7) and (11)) but with an uncertainty large enough to encompass the results of Table III, i.e., 5’: = (127 + 4) cm-’ atm-’ at 295.7 K. (13) DISCUSSION

Table IV shows our final result for the v., integrated band strength, corrected to a temperature of 300 K, in comparison with other recent determinations (#a, S-10). There are compelling reasons for accepting our value of the band strength in preference to the earlier diode laser results, We have studied many more lines, over a much wider range of J, Fox et al. (4) and Restelli et al. (5) investigated 6 and 10 lines respectively, in contrast to our 49 lines extending from R( 1) to P(20). Although few details are given, neither previous diode laser study appears to have devoted much attention to the corrections needed for pressure-broadening or diode laser lineshape; these corrections can together amount to several percent (cf. the

v+ BAND STRENGTH

377

OF ‘*CH4

TABLE IV Recent Determinations of the v4 Band Strength in “CH, -2 sl+~/cm am -I

Instrumental

Resolution

Integration

at 300 K

technique

(cm-')

method

Reference

104 * 6

Diode laser

10-4

Vib-rot model

Fox et aZ. (4)

116 r 3

Diode laser

w-4

Vib-rot

Restelli et a$. (5)

I25 t 4

Diode laser

10-4

Vib-rot model

model

This work

129 f 2

Grating spectrometer

1.0

High pressure

Bode & Smit (8)

132 f 7

Grating spectrometer

0.2-0.3

Line summation

Ko & Varanasi (9)

Fourier transform

0.06

Line sumnation

Lutz

166 * 17

et az. (6)

corrected line strengths of Table I with the preliminary uncorrected line strengths of the corres~nding lines reported by Jennings (I1 )). Perhaps the most important point, however, is that both previous sets of diode laser results show evidence of potential systematic errors. It has been noted already (12) that the four measurements of R -( 5) F,( 1) and R -( 5) F2 by Fox et al. (4) exhibit a wide spread-25% of the mean value of these four measurements-whereas the experimental error was expected to be around 6%. Restelli et al. (5) reported line widths some 10% greater than the calculated Doppler widths, indicating considerable problems with their diode lineshape. Nevertheless the relative intensities measured by Restelli et al. seem to be very satisfactory. If the line strengths reported by Restelli et al. are all multiplied by 1.09, nine of their ten lines are brought into excellent agreement with the pr~ictions of our best intensity model (the exception being the rather weak Q*(12) F,(3) line near 1306.0 cm-‘). In the case of the measurements of Fox et al. the scatter in relative intensity between the observations and the predictions of our model is much greater. There are also good reasons for doubting the very high band strength obtained by Lutz et al. (6). Lutz et al. give an interesting comparison between their work and that of Ko and Varanasi (IO), showing that the two sets of line strength sums agree very well in the P and R branches of v4_Lutz et al. differ strongly from Ko and Varanasi in the Q branch of u4, finding almost twice the integrated intensity. This “extra” Q-branch intensity is almost entirely responsible for the marked difference in the derived band strengths, i.e., 166 cmm2 atm-’ at 300 K (Lutz et al.) as against 132 cm-’ atm-’ at 300 K (Ko and Varanasi). Such an effect, if real, would be very hard to understand theoretically (there is no sign of any comparable effect in the well-studied v3 band of CH4 (20,23)) and we believe that the apparent extra Q-branch intensity must be an artifact of the experiment or the data reduction procedure of Blatherwick et al. (7). Support for this belief comes from the earlier diode laser studies of Fox et al. (4) and Restelli et al. (5). Even though we have reservations over the precision of these studies, as stated above, both sets of results

378

JENNINGS AND ROBIETTE

would seem to rule out an enhancement of Q-branch line strengths over those of P- and R-branch lines on the scale proposed by Lutz et al. In addition, preliminary results of a study by Brown et al. (24) based on spectra recorded at the Kitt Peak National Observatory interferometer show clearly that the Q-branch line strength measurements of Lutz and his collaborators (6,7) are often seriously in error where blended lines are involved. There remain three recent band strength determinations which are mutually consistent, i.e., those obtained in this work (125 rfr 4 crns2 atm-’ at 300 K), by Bode and Smit (129 rt 2 cm-’ atm-’ at 300 K (a)), and by Ko and Varanasi (132 3- 7 cm-* atm-’ at 300 K (9, 10)). The analysis of Brown et al. is not yet complete (24), but the results to date indicate a band strength of around 127 crnm2 atm-’ at 300 K. Since these four studies all employed different techniques-grating spectroscopy, diode laser spectroscopy, Fourier transform spectroscopy, and the classic Wilson- Wells-Penner- Weber high-pressure method-the agreement between them is very reassuring and suggests strongly that the u4 band strength is now known with a probable error of only 2-3s. The weighted mean value from our work and that of Bode and Smit (8) and Ko and Varanasi (10) is 128 + 3 cmF2 atm-’ at 300 K, and we consider this the best estimate currently available. It should be noted, however, that the interferometric measurements of Brown et ai. (24) should be capable of yielding still better results when the full range of data in their spectra has been treated. Higher-order effects in the Herman-Wallis factor form another topic which deserves future attention. Our results show clearly that the linear m coefficient is of the sign and approximateiy the magnitude predicted by previous work (20, 22), but the high J P-branch lines are found ex~rimentally to be more intense than a first-order calculation of the Herman-Wallis factor would require. It must be emphasized, though, that the intensity model used is only approximate: itincludes the Coriolis interaction of u4 and v2 (by explicit diagonalization (12)) and that of vq with v3 (by perturbation theory (20)). The important Coriolis interaction of vz with v) has been omitted altogether. While the latter interaction would affect vz line strengths primarily, the v2 and v4 bands are so strongly coupled at high J that second-order effects of the vZ/v3 coupling on the v4 line strengths must certainly be present. The precision of the best line strength measurements (20, 24) is now su~ciently good to justify a three-band theoretical treatment of v2, v3, and v4, with all three Coriolis couplings calculated by matrix diagonalization. Without a model at this level of sophistication, the more subtle line strength effects in the v2/v4 region (e.g., the intensities of v2 lines and the m2 dependence of vq intensities) should be interpreted with caution. ACKNOWLEDGMENTS We wish to thank L. L. Strow for valuable discussions concerning the correction of line strengths for pressure and diode lineshape effects, and also J. L. Faris and J. J. Hillman for laboratory support. We are also grateful to Linda R. Brown for communicating results prior to publication, and for other helpful comment on the experimental and theoretical aspects of this problem. RECEIVED:

March

9, 1982

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A. K. D. K. G. 6. B. 7. R. 8. 9.

10. II. 12. 13.

14. 15.

16. 17. 18.

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19. W. B. OLSON,A. G. MAKI, AND W. J. LAFFERTY,J. Phys. Chem. Ref Dafa IO, 1065-1084 (1981). 20. M. DANG-NHU, A. S. PINE, AND A. G. ROBIETTE,J. Mol. Spectrasc. 77, 57-68 (1979). 21. A. G. ROBIETTEAND M. DANG-NHU, J. Quant. Spectrosc. Radiat. Transfer 22,499-501 (1979). 22. A. G. ROBIE~E AND I. M. MILLS, .I. Mol. Speetrosc. 77,48-56 (1979). 23. D. L. GRAY, A. G. ROBIE~E, AND A. S. PINE, J. Mol. Spectrosc. 77, 440-456 (1979). 24. L. R. BROWN,J. S. MARGOLIS,R. W. NORTON,AND B. A. STEDRY,to be published;L. R. BROWN, private communication(1981).